Generalized adaptive partition-based method for two-stage stochastic linear programs with fixed recourse

Cristian Ramirez-Pico, Eduardo Moreno

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We present a method to solve two-stage stochastic linear programming problems with fixed recourse when the uncertainty space can have either discrete or continuous distributions. Given a partition of the uncertainty space, the method is addressed to solve a discrete problem with one scenario for each element of the partition (subregions of the uncertainty space). Fixing first-stage variables, we formulate a second-stage subproblem for each element, and exploiting information from the dual of these problems, we provide conditions that the partition must satisfy to obtain an optimal solution. These conditions provide guidance on how to refine the partition, iteratively approaching an optimal solution. The results from computational experiments show how the method automatically refines the partition of the uncertainty space in the regions of interest for the problem. Our algorithm is a generalization of the adaptive partition-based method presented by Song and Luedtke for discrete distributions, extending its applicability to more general cases.

Original languageEnglish
Pages (from-to)755-774
Number of pages20
JournalMathematical Programming
Volume196
Issue number1-2
DOIs
StatePublished - Nov 2022

Keywords

  • Adaptive partition-based approach
  • Continuous distribution
  • Scenario aggregation
  • Two-stage stochastic programming

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